Planar Pop-Up Actuator Device with Embedded Electro-Magnetic Actuation

ABSTRACT

A planar actuator device, including a base plate including a first, second, and third pair of planar coils, each pair of planar coils having an inner coil and an outer coil, each pair of planar coils arranged along a first, second, and third linear motion axis, respectively, the first, second, and third linear motion axis arranged in a star configuration, and an actuation mechanism including a first, second, and third planar legs and a centerpiece, the first, second and third planar legs pivotably connected to the centerpiece, the planar legs including a first, second, and third sliding element and a first, second, and third middle section, respectively, a sliding element and middle section of a respective leg pivotably connected to each other, each sliding element including a permanent magnet.

FIELD OF THE INVENTION

The present invention is directed to the field of mechanical actuators,mechanical actuator for robots and haptic devices, and methods of usingand manufacturing the same devices.

DISCUSSION OF THE BACKGROUND ART

In the field of mechanical actuators and robots, the smart compositesmicrostructure (SCM) emerged as a high performing low cost innovativetechnique for manufacturing thin composites embedding many functionalfeatures such as electrical connections, actuators and sensors.Researchers demonstrated the potential of this novel manufacturingtechniques by realizing different origami inspired robots capable ofperforming different tasks including shape transformation, crawlinglocomotion, jumping and multimodal locomotion. In smaller scales, thismanufacturing technique has also been used to develop millimeter scaleflying robotic insects. For such actuators and robots based on SCM,piezoelectric actuators have been discussed to provide higher speeds (10mm/s to 50 mm/s) but due to their limited stroke they require the designof a complex transmission mechanism for their employment.

In addition, numerous literatures describe the design and fabrication ofcoupled magnet and coils and their miniaturized systems in the mesoscaleand in the microscale. Their advances have been apparent in wirelesspower transmission, tactile sensors, and medical imaging. For actuationpurposes, millimeter or sub-millimeter scale motions have been obtainedby exploiting, in many cases, the simple axial repulsion of a planarcoil and an axially magnetized cylindrical magnet.

However, despite these advancements in the field of mechanical actuationand robots, in particular devices and systems of reduced scale, stillfurther improvements and solutions are desired.

SUMMARY

According to one aspect of the present invention, a planar actuatordevice is provided. Preferably, the planar actuator device includes abase plate including a first, second, and third pair of planar coils,each pair of planar coils having an inner coil and an outer coil, eachpair of planar coils arranged along a first, second, and third linearmotion axis, respectively, the first, second, and third linear motionaxis arranged in a star configuration, and an actuation mechanismincluding a first, second, and third planar legs and a centerpiece, thefirst, second and third planar legs pivotably connected to thecenterpiece, the planar legs including a first, second, and thirdsliding element and a first, second, and third middle section,respectively, a sliding element and middle section of a respective legpivotably connected to each other, each sliding element including apermanent magnet. In addition, preferably, the first, second and thirdcoil pairs respectively, are configured for magnetic coupling with arespective permanent magnet of the first, second, and third slidingelement, respectively, to move the first, second, and third slidingelement along the first, second, and third linear motion axis,respectively.

According to another aspect of the present invention, an actuator deviceis provided. Preferably, the actuator device includes a base plateincluding a first, second, and third pair of planar coils, each pair ofplanar coils having an inner coil and an outer coil, each pair of planarcoils arranged along a first, second, and third linear motion axis,respectively, the first, second, and third linear motion axis arrangedin a star configuration, and an actuation mechanism including a first,second, and third planar legs, the planar legs including a first,second, and third sliding element and a first, second, and third middlesection, respectively, a sliding element and middle section of arespective leg pivotably connected to each other, each sliding elementincluding a permanent magnet. Moreover, the actuator device preferablyfurther includes a delta robot structure including a first, a second,and a third articulated arm and a centerpiece pivotably connected toeach of the first, second, and third articulated arm, each of the first,second, and third articulated arm having a lower section and an uppersection pivotably connected to each other, each end portion of thefirst, the second, and the third middle section of the first, thesecond, and the third leg, respectively, pivotably connected to thelower section of the first, second, and third articulated arm,respectively.

The above and other objects, features and advantages of the presentinvention and the manner of realizing them will become more apparent,and the invention itself will best be understood from a study of thefollowing description with reference to the attached drawings showingsome preferred embodiments of the invention.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The accompanying drawings, which are incorporated herein and constitutepart of this specification, illustrate the presently preferredembodiments of the invention, and together with the general descriptiongiven above and the detailed description given below, serve to explainfeatures of the invention.

FIGS. 1A, 1B, and 1C show a side and top schematic view of an aspect ofthe present invention, showing the pop-up foldable actuator with andwithout the articulated mechanism. FIG. 1A shows the unfolded and flattwo-dimensional (2D) configuration of the device with a top and the sideview, FIG. 1B shows the three-dimensional (3D) folded configuration uponan actuation with a top and side view, the arrows mark the direction ofmotion of sliding elements and centerpiece, and FIG. 1C shows the baseplatform without the articulated mechanism;

FIG. 2 shows a side schematic view of a miniaturized electromagneticactuator that represents the operating principle and components of thepop-up foldable actuator, the arrows mark the magnetization direction ofmagnet and coils;

FIG. 3 shows a schematic perspective view of the layers that can formthe pop-up parallel actuator device;

FIG. 4A shows a schematic perspective view of the pop-up parallelactuator device the unfolded in the 2D state at the left, and the folded3D device configuration on the right, FIG. 4B shows a variant of a baseplatform with three openings and corresponding pairs of planar coilsforming linear motion axes that are not arranged in star configuration.FIG. 4C shows another variant of a base platform with five (5) openingsand corresponding pairs of planar coils forming five (5) linear motionaxes that are arranged in pentagon configuration, and FIG. 4D shows avariant of a base platform with four (4) openings and correspondingpairs of planar coils forming four (4) linear motion axes.

FIG. 5 shows a schematic representation of the two-position slidermechanism, the proposed device can be considered axial symmetric andcomposed by three (3) sliders arranged at 120° from each other andsharing the prismatic joint;

FIG. 6A shows a schematic perspective representation of the assembledminiaturized electromagnetic actuator used for the pop-up foldableactuator, with. The schematic of the assembled actuator, and FIG. 6Bshows a schematic perspective representation of the different layers ofthe device shown in FIG. 6A that compose the miniaturizedelectromagnetic actuator used for the pop-up foldable actuator, FIG. 6Cshows an exemplary opening with three planar coils that can form asingle linear motion axis, instead of two planar coils described in FIG.6A, FIG. 6D shows an exemplary opening with five (5) planar coils thatcan form a single linear motion axis, the five (5) planar coils beingoverlapping with each other;

FIG. 7A shows a graph schematically representing magnet-coilinteractions, showing a coordinate reference system used for definingthe position of the magnet in respect to the coils in the upper section,and the resultant force acting on the magnet for increasing X positionsin the lower section, FIG. 7B schematically depicts a graph withcalculated finite element method (FEM) resulting forces in X and Zdirection by changing magnet X position, and FIG. 7C depicts a 3D graphwith FEM resulting forces in X direction by changing magnet X positionand magnet elevation along Z in the upper section, and depicts a 3Dgraph FEM resulting forces in Z direction by changing magnet X positionand magnet elevation along Z direction in the lower section;

FIG. 8 shows top views from a masks and coils made from the mask, and acomparison of mask and corresponding resultant coil that can be used forthe pop-up foldable actuator. In the manufactured coil an underetchingeffect is visible, and conductor tracks result much thinner than thecorrespondent mask tracks;

FIG. 9 depicts a schematic perspective representation of an exemplarypop-up foldable actuator in pop-up (left) and extended (right)configurations and exemplary design parameters used. The values of theparameters used are shown in Table II;

FIG. 10 shows two photographs of the pop-up foldable actuator showingalignment holes used during the fabrication process. The device is shownin a flat, collapsed state (left), and in the pop-up state (right);

FIG. 11 shows a schematic top view of an exemplary pop-up foldableactuator according to an aspect of the present invention with someexemplary dimensions, the weights of the components shown in Table III;

FIG. 12 is a schematic representation of a free body diagrams of thethree links composing the triple slider mechanism of a pop-up foldableactuator;

FIGS. 13A-13B show perspective views of the actuator coils and asymbolic representation of one or two hall effect sensors to measuretime constants of the coils, and FIG. 13C shows a system for theverification of single rail dynamics including a high speed camera, apop-up foldable actuator device equipped with a tracking marker, and apower supply;

FIG. 14 shows a graph with the magnetic field development as a functionof time for actuation voltage of 20 V and 30 V confirming a negligibleelectromagnetic transient response;

FIG. 15A shows a graph representing normalized magnetic flux densitydecrease due to thermal increase in simulation, FIG. 15B shows a graphwith experimental results thereof, and FIG. 15C shows a graphrepresenting a B field expected decrease per second for different inputvoltages for the actuator;

FIG. 16A-16C show graphs depicting a position of the slider in the rail,with FIG. 16A showing the Fx for different positions along the rail,FIG. 16B showing different voltages as a function of magnet position intime, and FIG. 16C shows calculated parameters used in the comparisonwith the model;

FIGS. 17A-17D show graphs that represent the comparison of the magnetmotion calculated parameters, with FIG. 17A showing maximum speed, FIG.17B showing the maximum position, FIG. 17C showing the final position,and FIG. 17D showing motion time. The simulation results are providedwith the lines having the circles, and experimental results the lineswith the dots, the error bars are calculated on the standard deviationof three repetitions;

FIG. 18A-18B show schematic perspective views of the pop-up foldableactuator device that has been used for experimental purposes and tests,showing in FIG. 18A a marker for each leg of the actuator device, and inFIG. 18B a mass placed on the top platform of the actuator device forpayload tests;

FIG. 19A-19C depicts graphs representing performance measurements of thepop-up foldable actuator device, showing a top platform position in FIG.19A, top platform speed in FIG. 19B, and top platform acceleration inFIG. 19C;

FIG. 20A-20C depicts graphs representing performance including the masson the top platform, by testing different payload weights, showing a topplatform position in FIG. 20A, top platform speed in FIG. 20B, and topplatform acceleration in FIG. 20C, also describing the minimum elevationand power supply voltage to initiate the motion;

FIG. 21A-21D depicts graphs showing a comparison of the motionparameters of an exemplary pop-up foldable device, based on experimental(dot) and simulated (circle) results, including maximum speed in FIG.21A, maximum position in FIG. 21B, final position in FIG. 21C, andmotion time in FIG. 21D;

FIG. 22 shows a photo of an exemplary pop-up foldable actuator device inan experimental system for a steady forces test, the system including aforce sensor and a micro stage placed on top of the platform of thepop-up foldable actuator device;

FIG. 23 shows a graph with the experimental results of the system shownin FIG. 22, depicting experimental and simulated results of force as afunction of elevation;

FIGS. 24A and 24B depict graphs representing achievable speeds andpositional ranges for the top platform of the pop-up foldable actuatordevice, based on simulation results, for different weights placed on tothe platform or centerpiece, and power supply voltages;

FIG. 25 shows a schematic perspective view of another embodiment of thepop-up foldable actuator device, where a delta robot is interfaced theactuator legs, showing the device in a folded portable configuration onthe left, and 3D pop-up configuration on the right; and

FIG. 26A-26C shows a schematic perspective views of the pop-up foldableactuator device on a slidable tray integrated into a laptop computer(FIG. 26A), into a tablet (FIG. 26B), and into a smart phone (FIG. 26C),according to still another aspect of the present invention.

Table I shows user-defined parameters used in the FEM simulations for anexemplary pop-up foldable actuator device;

Table II shows design parameters for an exemplary pop-up foldableactuator device;

Table III shows the weight of the different parts for an exemplarypop-up foldable actuator device;

Table IV shows parameters used in the thermal model for an exemplarypop-up foldable actuator device; and

Table V shows dynamic parameters used in magnet in rail model for anexemplary pop-up foldable actuator device.

Herein, identical reference numerals are used, where possible, todesignate identical elements that are common to the figures. Also, theimages are simplified for illustration purposes and may not be depictedto scale.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1A depicts a top and side schematic view of a pop-up planaractuator device 100, according to one aspect of the present invention.The device 100 includes a base platform 10 and an articulated mechanism70 having three (3) legs 30, 40, 50 each rotatably connected at one endto a top platform 80. Top platform or centerpiece 80 can have asubstantially triangular shape or another shape that has three (3)sides, each side rotatably connecting to a corresponding end of a leg30, 40, 50. Each leg 30, 40, 50 includes a respective slider 32, 42, 52and a respective permanent magnet 34, 44, 54 that are arranged at theother end of the corresponding leg 30, 40, 50. Each permanent magnet 34,44, 54 is axially magnetized and can be surface-mounted to correspondingleg 30, 40, 50. Each slider 32, 42, 52 is rotatably connected at an endportion to a middle section of a corresponding leg 30, 40, 50. Asfurther shown in FIG. 3, base platform 10 includes three (3) railstructure 13, 15, 17, rail structures 13, 15, 17 defined as side wallsof longitudinal, flat openings 12, 14, 16, each opening 12, 14, 16having a shape or outline to accommodate a corresponding leg 30, 40, 50when the device 100 are in a disengaged or deactivated state. This meansthat legs 30, 40, and 50 are in a planar or flat state. Moreover,openings 12, 14, 16 are arranged in a star configuration towards eachother, and at the center of the star an opening 18 is arranged toaccommodate the top platform 80, when device 100 is in the disengaged ordeactivated state, as shown in FIG. 1A.

The mechanical moving elements or articulated mechanism 70 that includelegs 30, 40, 50 with slider 32, 42, 52, respectively, arranged in a starconfiguration around centerpiece 80 can be made from one layer.Rotatable connections are formed between each slider 32, 42, 52 of leg30, 40, 50 and middle sections of leg 30, 40, 50, and between eachmiddle section of leg 30, 40, 50 and top platform or centerpiece 80.These rotatable connections can be made by a thinned portion as afoldable linkage from a single layer of carbon fiber. In a variant, thearticulated mechanism 70 can be made of reinforced epoxy to manufacturelegs 30, 40, 50 and centerpiece 80, that are connected together with athin polyamide layer forming the rotatable connections.

FIG. 1C shows the base platform 10 with the articulated mechanism 70removed therefrom. In the base platform 10 at an area of each opening12, 14, 16, pairs of planar coils 22, 23, 24, 25, and 26, 27 arearranged, such that an outer planar coil 22, 24, 26 of the pair of coilsis arranged at an outer section of a corresponding opening 12, 14, 16,and the inner planar coils 23, 25, 27 of the pair of coils are arrangedaway from the outer section of the corresponding openings 12, 14, 16closer to the center of the star. FIG. 1B shows the outer planar coils22, 24, 26 partially uncovered by an articulated mechanism 70 andcorresponding slider 32, 42, 52 of leg 30, 40, 50, respectively, whenthe device 100 is in an engaged or activated state. Pairs of planarcoils 22, 23, 24, 25, and 26, 27 are used to activate a linear movementof a corresponding slider 32, 42, 52 in the corresponding opening 12,14, 16 with a corresponding permanent magnet 34, 44, 54 that is arrangedon slider 32, 42, 52, respectively. Pairs of planar coils are spacedapart by a distance D1, D2, and D3, respectively, preferably thedistance D1, D1, and D3 being the same. The distances D1, D2, and D3defines the range of linear motion for corresponding sliders 32, 42, and52, and in turn define a motional range of centerpiece 80.

Thereby, each pair of planar coils forms a linear motion axis L1, L2,and L3, respectively, with coils 22, 23 arranged along the linear motionaxis L1, coils 24, 25 arranged along linear motion axis L2, and coils26, 27 arranged along linear motion axis L3. In the variant shown, thelinear motion axes L1, L2, and L3 are arranged in a star configurationcrossing each other at a middle point, preferably located substantiallyin a center of the base platform 10. However, other types of arrangementof the linear axes is also possible. Thereby, pairs of planar coils 22,23, 24, 25, and 26, 27 and corresponding legs 30, 40, 50 and theassociated slider 32, 42, 52 form three linear actuators that can movesliders 32, 42, 52 along linear motion axes L1, L2, L3, respectively, bymagnetic coupling.

The linear actuators, placed in a star configuration on the baseplatform 10 and coupled mechanically together with the top platform orcenterpiece 80 include the pairs of planar coils 22, 23, 24, 25, and 26,27, a rail structure 13, 15, 17 that is formed by side walls of openings12, 14, 16 arranged in a star configuration, and an axially magnetizedpermanent magnets 34, 44, 54 arranged at a corresponding slider 32, 42,52. The pair of coils 22, 23, 24, 25, and 26, 27 are designed to makethe corresponding slider 32, 42, 52 with magnet 34, 44, 54 translate,move or slide along the opening in a direction of longitudinal extensionof each opening 12, 14, 16 when the pair of coils are energized thusobtaining a linear motion. Each leg 30, 40, 50 in this mechanismconstrains four (4) out of the six (6) degrees of freedom (DoF) of thetop platform or centerpiece 80. Because the constraints between each legare coupled, the overall mechanism consisting of three legs 30, 40, 50has one (1) active DoF. For example, when inner coils 23, 25, 27 areenergized, while outer coils 22, 24, 26 are not energized, top platformor centerpiece 80 moves to an outermost position away from the baseplatform 10, by a linear motion of all sliders 32, 42, 52 towards thecenter of the star arrangement of openings 12, 14, 16. In contrastthereto, as shown in FIG. 1A, device 100 is configured such that whenouter coils 22, 24, 26 are energized, while inner coils 23, 25, 27 arenot energized, top platform or centerpiece 80 moves towards the baseplatform 10 to be accommodated in opening 18, by a linear motion of allsliders 32, 42, 52 away from the center of the star arrangement ofopenings 12, 14, 16. At the same time, legs 30, 40, 50 move towards baseplatform 10 to be accommodated in openings 12, 14, 16. In thisdeactivated state, legs 30, 40, 50 and top platform or centerpiece 80are arranged in a same plane parallel to the extension of the baseplatform 10.

In FIG. 1A, device 100 is shown in a planar, flat, state, when device100 is deactivated or disengaged, and in FIG. 1B the device 100 is shownto be in a 3D state, where legs 30, 40, 50 connected to top platform 80protrude from base platform 10, in an operating or expanded state. Inthe deactivated state, it is possible that the legs 30, 40, 50 and topplatform 80 are entirely comprised by base platform 10, when seen fromthe lateral side, as shown on the top of FIG. 1A. According to someaspects of the present invention, these features allow to provide for apop-up planar actuator device 100 that can be used for highly mobile orportable robotics, or for a haptic device as a portable and collapsiblehuman-robot interface (HRI). The device 100 is very compact in adeactivated state to form a thin planar device, and it can bemanufactured based on a layered construction using printed circuit boardand surface mount fabrication process steps. Such manufacturing allowsto make the fabrication accurate, robust and comparativelycost-effective. In the embodiment shown in FIG. 1A, the entire device100 is less than 1.7-mm thick in its deactivated or disengaged state,yet the device 100 will increase to a multiple of the thickness in anactivated 3D state, as shown in FIG. 1B.

FIGS. 1A and 1B also show a power supply module 90 for providingelectrical power individually to each of the planar coils 22, 23, 24,25, 26, 27. This allows to magnetize each coil separately andindividually to create a magnetic coupling with permanent magnets 34,44, 54. Next, a control device 95 is shown that is configured to controlthe power supply module 90, and to receive measurement signals 97 fromthe device 100. For example, as discussed further below, hall effectsensors or position measurements sensors that are embedded in eitherbase platform 10 or articulated mechanism 70 can provide for feedbackmeasurement signals to control device 95, to provide for controlledelectrical power for each planar coil 22, 23, 24, 25, 26, 27 forgenerating linear motion of each sliding elements 32, 42, 52. In thevariant shown, the control device 95 and the power supply module 90 arearranged outside of the base platform 10. However, it is also possibleto integrate a planar power supply module 90 and/or a planar controldevice 95, for example a microchip, directly into the planar layers ofthe base platform 10.

With the aspects and features of device 100 used for example but notlimited to robotic technology, actuators, and haptic devices, it ispossible to achieve more challenging tasks in more sophisticated andspecial environments. Bringing traditionally powerful and fast, but as aconsequence, large and unsafe robotic systems and devices into dailyhuman life presents numerous engineering challenges. One aspect is theprovision of mechanical and geometric scalability of the traditionalmechanisms and actuators. In particular, portable robotic manipulatorsand highly interactive HRI require extremely demanding engineeringrequirements that oblige novel solutions in mechanism design andactuation systems. The structural bases for many robotic devices aremanipulators and grippers based on numerous linkages and joints.Therefore, with the features of pop-up planar actuator device 100,according to some aspects of the present invention, a mechanicallysimple yet scalable and effective design is proposed, that can be usedfor example as an HRI for existing systems and devices. In a deactivatedstate, the device 100 can be made very thin allowing specificapplications for handling, mobility, and use.

The device 100 according to some aspects of the present invention allowsto provide for a flat or planar miniature parallel system with anembedded actuation mechanism and the mechanical links for motiontransmission by a top platform and centerpiece 80 that can be lifted outfrom the planar state to perform 3D motions with three (3) degrees offreedom. According to another aspect of the present invention, device100 can be used as a component for a miniature haptic interface. Withpop-up planar actuator device 100, origami inspired designs based onfolding technique to give structural stability to thin lightweightcomposite materials while endowing possibility of transformation betweena planar deactivated, quasi-2D configuration to a 3D configuration ispossible. Moreover, pop-up planar actuator device 100 can bemanufactured in a foldable pocket size to a millimeter-thick structurethat can transform into robust 3D articulated mechanisms that allowsinteraction with a potential user by providing motion and/or force in adesired direction with the top platform 80.

With at least some aspects of the present invention, pop-up planaractuator device 100 includes a millimeter-thick linear electromagneticactuator, made of legs 30, 40, 50 with sliders 32, 42, 52, and permanentmagnets 34, 44, 54 and pairs of planar coils 22, 23, 24, 25, 26, 27 thatcan be further integrated into a robotic device or system, or can beintegrated into a haptic device. According to one aspect of theinvention, with an exemplary embodiment of device 100 the magnetic fieldis controlled that is generated by the pairs of planar coils 22, 23, 24,25, 26, 27 to modulate up to 13 mm actuation distance with a thicknessof 1.7 mm of the device 100 in the deactivated state. Device 100 alsodemonstrates the functionalities and performance on a one-degreeof-freedom (DoF) origami parallel platform that can be reversibly foldedfrom a planar, flat, 2D configuration to a 3D pop-up structure.

In order to make device 100 autonomous and to reduce the overall size ofthe device 100, device 100 and the articulated mechanism 70 can beembedded as one of the functional layers in SCM. Actuators to beembedded in the structure have to be thin, contained in the millimetersize of the system, and capable of a wide range of speed in a rangebetween 1 mm/s to 100 mm/s and forces of at least 200 mN, for example toallow interaction as a haptic device with human hands.

Currently, there are no suitable devices and systems for manufacturingand operating such device. Thermally-activated actuation methods,whether for permanent shape transformation or repeatable motion usingshape memory alloy (SMA) actuators are not suitable for such system anddevice given the need for fast and repeatable motions in human-robotinterfaces (HRI). Aiming to achieve an actuation system with a widestroke, high speed and low-profile, according to one aspect of thepresent invention, a device 100 is presented that allows to useelectromagnetic actuation due to the ease of manufacturing planar coils22, 23, 24, 25, 26, 27 through photolithography process and thepossibility of embedding these layers in a flat, planar or quasi-2Dstructure based on the SCM technique.

With FIG. 2, a schematic and simplified representation of the actuatorcomponents and the linear actuation operation principle is described,with a side cross-sectional view. In this description, only one leg ofthe device 100 is described for simplification purposes, but therepresentation of the operating principle shown in FIG. 2 applies to allthree (3) legs, or more legs. A permanent magnet 34 is shown as a partof a slider 32 that can move above a sliding surface 13 of opening 12formed by base platform 10. Below the sliding surface 12, a planar coilpair 22, 23 are arranged. The arrangement of coil pair 22, 23 defines amaximal linear translation range that can be achieved by actuator. Coils22 and 23 can be selectively energized so that permanent magnet 24 andcorresponding slider 32 can move to the left or the right to perform alinear movement along a longitudinal extension of opening 12.

FIG. 3 shows a perspective, exploded view of one embodiment of device100, in which device 100 is made of a series of thin layers, for exampleprinted circuit board layers that can be combined with reinforcementlayers, for example fiberglass or carbon fiber layers. In this variant,device 100 is made of a top rail layer 110 that provides for guidance ofthe legs 30, 40, 50 of the articulated mechanism 70, articulatedmechanism 70 itself with the permanent magnets 34, 44, 54. The legs 30,40, 50 of articulated mechanism 70 themselves can be made of multiplelayers, and each permanent magnet 34, 44, 54 located inside a cavitythat traverses all of the multiple layers that form the correspondingleg 30, 40, 50. Next, an inner rail layer 120 is shown that provides foradditional guidance for legs. Openings 12, 14, 16 for respective legs30, 40, 50 are formed by both the top rail layer 110 and the inner raillayer 120. This can be done with the opening of top rail layer 110 beingslightly narrower in a transverse direction of a corresponding linearmotion axis as compared to the opening formed by the inner rail layer120. For example, respective slider 32, 42, 52 having a respectivepermanent magnet 34, 44, 54 are slightly narrower in width W3 than thewidth W2 of the respective opening 12, 14, 16 formed by inner rail 120,such that the sliders 32, 42, 52 can be guided linearly along therespective opening, while a width W1 of the respective opening of toprail layer 110 is slightly narrower than a width W3 of the sliders 32,42, 52 so that the sliders can be guided and still cannot exit therespective opening 12, 14, 16 that form the respective linear motionaxis. In addition, a width W4 of leg 30, 40, 50 is narrower than thewidth W1 of the top rail layer 110, so that the legs 30, 40, 50 can exitand enter the openings 12, 14, 16, respectively, upon actuation of thesliders.

Next, the inner rail 120 is placed onto a stack of layered coils 130.The layered coils 130 can be a stack of printed circuit boards, or amultilayer printed circuit board that includes planar coils 22, 23, 24,25, 26, 27. In a variant, each coil 22, 23, 24, 25, 26, 27 can be madeof a single coil from each layer of the layered coils 130, and then thesingle coils are all connected in series or in parallel. The stack oflayered coils 130 is placed onto a bottom layer 140 serving as a cover.Materials of the layers 110, 120, 130, and 140 can be chosen to fortheir respective function. For example, the top rail layer 110 and thebottom layer 140 can be made of a thin and stiff material to serve as acasing, for example but not limited to a thin layer of carbon fiber,fiberglass, or metal. An inner side of top rail layer 110 can be coatedwith a layer that reduced friction, for example but not limit to Teflonor Kevlar™. Inner rail layers 120 can also be made to have innersurfaces that form the opening that provide for reduced friction towardsthe sliders 32, 42, 52. Similarly, an upper surface of layered coils 130that faces the sliders 32, 42, 52 can be covered with an thin insulatinglayer to preserve the magnetic coupling between the permanent magnets34, 44, 54, and planar coils 22, 23, 24, 25, 26, 27. The design andfabrication of layers 110, 120, 130, and 140 and articulated mechanism70 can be based on the SCM fabrication that embeds multiple essentialcomponents such as folding linkages and actuation system in thedifferent layers of the structure.

FIG. 4A shows the assembled pop-up planar actuator device 100 with thesliders 32, 42, 52 located and guided within their corresponding opening12, 14, 16, showing the device 100 on the left side in the deactivatedplanar or 2D configuration, with centerpiece or platform 80 accommodatedin device 100, so that the entire device 100 is entirely planar. On theright side of FIG. 4A, the activated device 100 is shown, where thesliders 32, 42, 52 have moved towards a center of device 100, and thecenterpiece 80 has been lifted from base platform 10, the base platform10 preferably being formed by layers 110, 120, 130, and 140 shown inFIG. 3. In the activated state, the device 100 is not planar anymore,and is in a 3D configuration.

According to another aspect of the present invention, the linear motionaxes can be arranged in different configurations, and there is no needto have exactly three axes. FIG. 4B shows another variant of the baseplatform 10, with openings having pairs of planar coils that definethree (3) linear motion axes, in which the three (3) motion axes arearranged in a triangular configuration. In other variant, as shown inFIG. 4C, five (5) linear motion axes are provided with five openings andfive corresponding pairs of planar coils, placed in a pentagonalarrangement. Moreover, another variant in FIG. 4D shows four (4) linearmotion axes are provided with four openings and four corresponding pairsof planar coils, placed in a substantially square arrangement.

Next, according to another aspect of the present invention, theperformance of the pop-up planar actuator device 100 is determined bythe geometrical parameters of the mechanism which dictate thetransmission ratio between the input and the output strokes, velocities,as well as by the effectiveness of different configurations. Designparameters for the overall platform based on these considerations arepresented. Regarding the kinematics of the mechanism of the pop-upplanar actuator device 100 as shown in FIGS. 1A-1C and 3, the resultingmechanism has been modelled of each leg as equivalent to a double sliderpresented in FIG. 5. In this configuration, the horizontal slider, link1, includes the magnet and its motion is controlled by the magneticfield generated by the coils. This link has a single degree of freedom(DoF) dictated by the rail in which it moves. The mechanism transformsthe in-plane motion of this link to the vertical motion of the secondslider, represented by link 3 through the interaction with the link 2.

The transmission ratio between the input link, link 1, and the outputlink, link 3, is determined by the length of the link 2 and the positionof link 1 in the rail according to the following Equations (1) and (2):

$\begin{matrix}{y_{3} = \sqrt{l^{2} - ( {l - x_{1}} )^{2}}} & (1) \\{\overset{.}{y_{3}} = {\frac{\overset{.}{x_{1}}( {l - x_{1}} )}{\sqrt{l^{2} - ( {l - x_{1}} )^{2}}} = \frac{\overset{.}{x_{1}}}{\tan \mspace{11mu} \theta_{2}}}} & (2)\end{matrix}$

The equation for the velocity of the links suggests a nonlineartransmission between the link 1 and link 3 velocities. In the flatstate, the mechanism is at a singular point and as it starts movingupwards the ratio of the output speed to the input speed decreasesaccording to Equation (2). This transmission ratio can be exploitedfurther to obtain a desired force profile on the output link. Decreasingthe velocity ratio, the mechanism has a higher force transmission inlarger angles that is desirable since it can overcome increasing forcesas it moves toward its final position.

The pop-up planar actuator device 70 is over-constrained with the threesliders 32, 42, 52. Despite the over-constraint, this design has twoadvantages. First, it reduces the forces transmitted to the rails,because the in-plane components of the three legs 30, 40, 50 exerted onthe centerpiece 80 cancel each other out, which reduces significantlythe friction forces onto the rails, and second, the output verticalforce from the centerpiece 80 is increased by increasing the number ofactuation points. Also, the over-constraint mechanism issues arealleviated via clearance between the leg 30, 40, 50 and the rail. Thedynamic modeling of this structure helps to understand the forces actingon the mechanism of the articulated mechanism 70, and other types ofarticulated mechanisms.

According to still another aspect of the present invention, anindividual linear actuator 200 of device 100 is described as shown inFIGS. 6A and 6B. In the variant shown a linear actuator 200 is composedof two planar coils 22, 23 that are made from layered coils structure230, a rail structure 13 that is formed by a side wall of top rail layer210 and a side wall of inner or lateral rail layer 220 that face opening12, thereby forming guiding rails for corresponding side edges of slider32, and an axially magnetized permanent magnet 34 that is mounted to theslider 32. For representation purposes, the corresponding leg 30 is notshown. The coils 22, 23 are designed in order to make the magnet 32slide in rail structure 13 that are formed by side walls of opening 12,when coils 22, 23 are energized. This allows slider 32 to move back andforth within opening 12, along linear motion axis LA1. With thedimensions shown, one advantage of this arrangement is that the magneticfield is managed along the rail to allow maximum of 8 mm stroke ofmovement along the linear motion axis LA1, but the transmission willredirect the stroke in vertical direction with leg 30 and centerpiece 80thus obtaining 13 mm actuation strokes of a 1.7 mm thick device 100.Accordingly, with the device 100, it is possible to obtain a ratiobetween the thickness of device 100 and the actuation stroke at about1:10, even 1:20. The linear movement of magnet 32 is initiated by thecombination of repulsive force from a first coil, either 22 or 23 andattractive force from the second coil, either 23 or 22. The magneticfields of the two planar coils 22, 23 interact and generate theelectromagnetic force on permanent magnet 32.

Although the magnetic forces applied to permanent magnet 32 drops withthe power of three (3) because it is dependent by magnet volume when themagnetic system is scaled down by reducing it in thickness for theplanar design of device 100, the force to weight ratio does not sufferfrom this reduction since the mass scales as well with the power ofthree (3). Furthermore, with the same current density in coils 22, 23,it is possible to reach higher actuation velocities. While decimeterscale coils use cylindrical wires, miniature planar coils, as shown inthe variant of FIGS. 6A and 6B, can use micron thick flat conductorswith rectangular cross section; this further increases the conductorsurface/volume ratio, boosting the thermal exchanges and as consequenceallowing higher current densities compared with the decimeter scalewhere thermal exchanges are not very efficient. As a consequence, upon ascaling of 1/k, increases the magnetic interaction of a factor k isincreased. See for example, Cugat, Orphee, Jerome Delamare, and GilbertReyne, “Magnetic micro-actuators and systems (MAGMAS),” IEEETransactions on magnetics 39.6 (2003): pp. 3607-3612. See also Niarchos,D, “Magnetic MEMS: key issues and some applications,” Sensors andActuators A: Physical 109.1 (2003): pp. 166-173, this reference beingherewith incorporated by reference in its entirety.

It has been shown to be difficult to obtain wide motions in millimeterscale by exploiting the axial repulsion of a planar coil and an axiallymagnetized cylindrical magnet, a challenge shared by other researchers.This is due to the exponential drop of magnetic forces with the increaseof a distance or gap between permanent magnet and coil. For this reason,the use of a linear electromagnetic actuator combined with propertransmission appears to be an ideal means of reducing the gap ordistance to a minimal value.

In an exemplary variant shown in FIGS. 6A and 6B, permanent magnet 32 isa 1 mm-long cylinder having a 10 mm diameter. It is axially magnetizedand has a magnetic flux remanence of 1.2 Tesla, for example from themanufacturer HKCM®. Coils 22, 23 are designed with slightly largerdiameter, 12 mm, the stroke will be smaller than the diameter of thecoil 22, 23 because, when the magnet is lying in the center of one ofthe two coils 22, 23, the repulsive or attractive forces would be normalto the direction of guiding rails 12 or normal to linear motion axis LA1and would not result in action of the mechanism. For these reasons wechose 8 mm to be conservative and ensure magnet motion. In this way, itis avoided that slider 32 with permanent magnet 34 lies directly in axiswith a coil 22, 23.

FIGS. 6C and 6D shows variants of the layered coils 230 that can be usedfor the linear actuator 200 of the pop-up planar actuator device 100.For example, FIG. 6C shows a layered coil with three instead of only twocoils, for a single linear motion axis LA1. Moreover, FIG. 6D shows fivecoils, adjacent coils having an overlapping surface area. This can bedone by arranging the two coils in the background in one layer, and thethree coils in the foreground in another layer, so that the multilayerstructure can be used to create overlapping magnetic fields with thecoils for linear actuator 200. With the addition of more coils that theminimal amount for operation of two coils, the magnetic field can begenerated more selectively along the linear motion axis LA1, and as aconsequence, a finer positioning of the sider 32 along axis LA1 ispossible.

In order to define the others system design parameters, finite elementsanalysis (1-BA) to evaluate the forces between coils 22, 23 and magnet34 has been executed using the AC/DC module of Comsol 5.2. The forcesapplied by the coils 22, 23 to magnet 34 have been considered, as firstapproximation, magnetostatic. For this purpose, a stationary study hasbeen set using the following Equations, with the Ampere law for staticcases defined as

∇×H−σv×B=J _(e)  (3)

The definition of magnetic potential is

B=∇×A  (4)

The constitutive relation for the magnet is

B=μ ₀μ_(r) H+B _(r)  (5)

The constitutive relation for the coils is

B=μ ₀μ_(r) H  (6)

And the externally generated currents for the coils are

$\begin{matrix}{J_{e} = {\frac{N\; I_{coil}}{a_{s}}{e_{coil}.}}} & (7)\end{matrix}$

The expression J_(e) of Equation (7) is an externally generated currentdensity, v is the velocity of the conductor, σ the electricalconductivity, H the magnetic field in Equation (3), A the magneticpotential in Equation (4), B is the flux density in Equation (6), Br theresidual flux density in Equation (5), μ₀ the magnetic permeability invacuum, μ_(r), the relative permeability of the material, N the numberof turns of the coil, I_(coil) the current energizing the coil, as isthe cross sectional area of the coil domain and e_(coil) is the coilcurrent flow.

A height of coil 22, 23 has been set to 0.5 mm to be embedded in amillimeter thick layered coil layer 230. The magnetic forces arecalculated using Maxwell's stress tensor, and in particular, a numericintegration on the surface of the object that the force acts upon, wasperformed (magnet). The aspect ratio of magnet 34 and coils 22, 23 wasaround 0.05 making computationally heavy meshing and solving the modelbut, we obtained a stable solution by using a gradient in mesh nodesdistribution and increasing elements number at around 106.

Magnet-coils interaction forces where tested for different positionsalong the linear motion axis LA1 and different elevations, and thesimulations were used set to evaluate the magnetostatic forces acting onmagnet 34. The interaction forces between the magnet 34 and another oneof the magnets 44, 54 at different distances have also been analyzed.The interactions of two magnets laying on a common plane and having aspecific distance between them was analyzed. This simulation has beenused set to evaluate the minimum distance for which two coplanar magnetsgenerate negligible interaction forces. With these results, the pop-upplanar actuator device 100 has been designed.

Regarding the magnet-coils interactions, a parametric study has beendone varying magnet position in x and y directions according to thereference system reported in FIGS. 7A and 7B. In the simulation, thecurrent and the conductor turns have been iteratively simulated, alongwith the maximum number of coil turns that were possible to bemanufactured with a given number of layers of layered coils 230. Theconstants used in the model are reported in Table I. Simulation resultswere used to estimate the ampere/turns needed to perform motion thusgetting an indication of the number of turns and layers for the planarcoils design with layered coils 230. The magnetostatic forces calculatedwith the simulations were used for the system motion prediction.

The parametric study that considering magnet position along the z axis;this was useful since magnet elevation depends by the platform design;the simulations results are reported in FIG. 7C. With exemplary device100 as shown in FIG. 10, the exemplary coils-magnet distance in the zdirection is 1.4 mm. Regarding the magnet-magnet interaction, anotherparametric study of two coplanar magnets was performed, varying theirdistance. According to the simulations, at a distance of 45 mm theinteraction forces between the magnets were lower than 0.1 mN, threeorders of magnitude lower than the maximum force applied by the coilsystem, for example 50 mN, therefore they can be considered negligible.We then considered this distance limit in the design of the pop-upparallel platform in order to avoid magnetic interactions between thelegs.

According to still another aspect of the present invention, a method formanufacturing the pop-up planar actuator device 100 is presented. Onegoal of the manufacturing method is to keep the overall dimension of theplatform at the minimum while maximizing the output force and the rangeof motion. This requires an accurate, robust and repeatable steps forthe manufacturing method to realize all the individual layers and tointegrate them. Next, the fabrication of coils 22, 23, 24, 25, 26, 27and articulated mechanism 70 and the integration of them in millimeterthick actuated pop-up planar actuator device 100.

For the planar coils, a photo-engraving technique on Pyralux™ flexiblethin sheets having a thickness of 32 μm with a conductor thickness of 12μm has been used. The winding sense of the stacked coils was inverted tosum the magnetic field produced by the single coils. To electricallyconnect in series overlapping coil layers in the layered coils 230, a UVlaser micromachining system was used, DCH-355-4 laser head fromPhotonics Industries Inc., to remove the Kapton™ layer from the back ofthe coil, exposing the conductor and then conductive epoxy glue wasapplied, for example Chemtronics™ CW2460 to electrically bond sixadjacent layers for the layered coils 230.

As one goal is to minimize the overall thickness of device 100 whiletargeting high actuation speeds, the initial criteria for maximizing theproduced magnetic field is to maximize the number of turns in a coil ofa single layer without stacking too many layers, thus, the conductivepath width was minimized avoiding short circuits and open circuits, andto connect the single coils throughout the layers in series. Thephotoresist has a 15 μm resolution; therefore, coils with a path widthof 50 μm and a distance between two turns of 100 μm have beeninvestigated.

As the first step, the coil shape was defined in Matlab′ from MathWorks™as a sequence of coordinates and the shape was further elaborated withAltium™ designer for printing the mask used for the circuit impression.The parameters such as the ultra-violet (UV) exposition time, thephotoresist development time and the etching time were iterativelychanged in order to increase the successful rate of the coils. Further,in order to compensate for the under-etching, masks with different paththicknesses were tested and the results were compared. As example, someof the masks used and resulting coils are shown in FIG. 8. The criteriafor choosing the fabrication parameters were the electrical resistanceexperimental values closeness to the theoretical calculated, and a lowpercentage of failures, considering as failed a coil with brokenconductors or with resistance deviating of 20% or more from thetheoretical values. The resistance of the coil was estimated accordingto the formula R=ρ*L/A, where ρ is copper resistivity (1.68 e-8 Ω/m), Lis the length of the conductor of the planar coil, calculated as 1.122 mfor the used coils of 12 mm in diameter and having 55 turns, and A isthe section of the conductor corresponding to a width between 50 μm and80 μm. It has been shown that a mask having 70 μm for the conductivepath and 30 μm for the insulating path gave the most robust results,with 20.9±3.2Ω where the theoretical value was 22.5Ω, and has been usedfor the steps of manufacturing the coils.

The dimensions of the mechanism were designed to have negligibleinteraction from the magnetic field of each two legs. The design wasbased on simulations that use the predetermined design parameters: themagnet size (10 mm in diameter), the magnet in rail motion range (8-10mm) and the diameter of the coils (12 mm). The minimum distance d, whichis the minimal distance of the magnets 34, 44, 54 at the pop-up state,of 45 mm was required. This initial design, used to study the behaviorof the system, follows the criteria of low weight and avoidance ofmagnet-magnet interactions.

As schematically shown in FIG. 9, the distance between the center of theplatform and center of the magnet during motion, a_(min), resultedaround 20 mm, being d=45 mm based on simulation results, because theactuation range was 8 mm, the length a_(max) in mechanism extendedconfiguration was 28 mm. The minimum length b, of the structureembedding the magnet was 12 mm, considering 1 mm of material around themagnets 34, 44, 54; the same size for, r_(p), central structure size (6mm) was maintained. Consequently, a value of c=a_(max)−r_(p)−b/2, 16 mmto the length c of the articulated link was assigned. The vertical rangeof motion of the platform was expected to be 12 mm.

Experimental results have been performed with the pop-up planar actuatordevice 100. An exemplary device 100 was made by integrating layers ofdifferent materials with specific functionalities for obtaining amultifunctional composite. The exemplary device 100 was composed of thefollowing functional layers, with reference to FIG. 3: Bottom layer 140that provides anchoring plane for the platform and protects sensitivelayered coils 130, layered coils 130 that provide magnetic fields forthe actuation. Two patterned glass fiber layers with a Kapton™ layerembedded between them provide for the articulated mechanism 70. Fourglass fiber layers that cover the coil system and form the rails for thesliders of the mechanism, by forming top rail layer 110 and inner raillayer 120.

FIG. 3 shows the schematic of the layers, FIG. 10 shows a picture of anexemplary device 100, and FIG. 11 reports platform size and weight.Table III reassumes platform elements mass. The patterns were machinedin different layers including the structural 0.2 mm glass fiber layers,the 32 μm coil layers and the 25 μm Kapton™ layers. These layers werealigned and stacked using the reference holes and a jig. Moreover, thelayers were connected with thermo-adhesive inter-layers using aheat-press. The resulting device 100 shown in FIG. 10, has a thicknessof 1.7 mm, in the collapsed state.

To identify the predominant physical effects influencing mechanismmotion, the coil system, the actuator, and the pop-up parallel platformwere analyzed and modelled. We estimated and experimentally verified thecoils time response, the temperature change and the friction between theslider and the rail. The pop-up planar actuator device 100 is poweredthrough multiple planar coil stacks, for example the layered coils 130.In the following paragraphs, an estimation of the coil system timeresponse has been made, and the experimental results are provided. Forverifying the time constant of the stacked coil system of layered coils130, coil inductance was calculated and experimentally verified thecorresponding value.

As the first approximation, the coil has been assumed as a series ofloops with the same diameter, and the theoretical formula used forestimating the inductance L_(circle) is:

$\begin{matrix}{L_{circle} \approx {N^{2}R\; µ_{0}{µ_{r}\lbrack {{\ln \; \frac{8R}{a_{l}}} - 2} \rbrack}}} & (9)\end{matrix}$

In Equation (9), N is the number of turns, R is the radius of thecircle, a₁ is the wire radius, μ₀ and μ_(r) are the magneticpermeability in vacuum (μ₀=1.2567 H/m) and the relative permeability ofthe medium, in this case, the air (μ_(r)=1.00000037). An inductance of1.4161 mH resulted from six coils that are connected in series having300 turns, 50 μm of conductor width and an average radius of 6 mm. Aresistance of 21Ω for each layer was considered. The resulting timeconstant, τ, was 11.2 μs. Because the calculation was based on actuationtimes at around 0.1 s electromagnetic transient effects were neglecteddue to magnetic field generation. Transient thermal response is anotheraspect that can change the magnetic field by affecting the electricalresistance of the coils. For describing this effect, we used the linearcorrelation between the temperature increase and the resistanceincrease:

R=R ₀[1+∝(T−T ₀)]  (10)

Where the electrical resistance, R, at the temperature, T, depends onthe resistance R₀, at the temperature T₀, and on the temperaturecoefficient α. Further, considering the power consumption after themagnetic field reaches the steady state, the power P, converted toelectrical energy due to the current I, flowing in the resistance,results in:

$\begin{matrix}{P = \frac{V^{2}}{R}} & (11)\end{matrix}$

While the temperature increase dT, due to the heat dQ, supplied to theconductor is:

dQ=Pdt=(m _(c) c _(c) +m _(k) c _(k))dT  (12)

where m_(c) and m_(k) are the mass of the conductor and the mass of theKapton™ in contact with the conductor, c_(c) is the specific heat of thecopper and c_(k) is the specific heat of the Kapton™. By multiplyingEquation (11) for the activation time t and integrating Equation (12),the following equation is obtained:

$\begin{matrix}{{( {{m_{c}c_{c}} + {m_{k}c_{k}}} )\lbrack {{{T^{2}\frac{\propto}{2}} + {T( {{1 -} \propto T_{0}} )} - T_{0} +} \propto \frac{T_{0}^{2}}{2}} \rbrack} = {\frac{V^{2}}{R_{0}}t}} & (13)\end{matrix}$

Solving Equation (13), the temperature T of the coil after a time t wascalculated, the values used for the constants are reported in Table IV.

Thermal exchanges have not been considered because the heating rate ofthe coil was expected to be fast and the materials the coil is incontact with do not have high thermal conductivity, i.e. Kapton™ andglass fiber. Although the proposed model is expected to overestimate thetemperature increase of the coil, the trend of current decrease due tothe temperature rise is expected to be similar to the experimental case.

Next, the rail and slider model is presented in the form of actuator200. Actuator 200 is tested in simulations, in particular theinteraction of magnet, the couple of coils that are energized inopposite sense, and the rail constraining magnet motion. The model wasused to identify the parameters affecting the rail and sliderinteraction. These parameters were evaluated using the experiment on oneactuator and they were then used to predict the motion of pop-up planaractuator device 100.

The main forces acting on the magnet are the magnetic forces applied bythe coils to the magnet considered dependent by their relative positionand by the current flowing in the coils; the interaction of the magnetwith the rail, modeled with static and dynamic dry friction where theforce generating friction is the magnetic component perpendicular to thedirection of motion and also the weight of the magnet; the constantforce C opposite to the direction of motion exerted by the bottom partof the rail on which the magnet slides.

The following equations describe actuator behavior:

F _(mX) −F _(fr) −C=m{umlaut over (x)}  (14)

F _(fr)=sign(x)(F _(mZ) +mg)μ_(n)  (15)

F _(mX) =f(x,V)Q,F _(mZ) =f(x,V)Q  (16, 17)

In these Equations, F_(mX) and F_(mZ) are the magnetostatic forces inthe direction of motion and in the direction perpendicular to coilplane. F_(mX) and F_(mZ) are function of the magnet position x, thepowering voltage V and the coil quality factor Q, ranging from 0 to 1,for taking into account the coil turn loss by leakages of the conductiveglue during the multilayer bonding. The values of the magnetic forceswere obtained by lookup tables over the FEM pre-calculated results. Theconstant m is the mass of the magnet moving into the rail, g thegravitational acceleration, F_(fr) is the friction force and μ_(n) isthe friction coefficient. To determine the unknown parameters μ_(n) andC in Equations (14) and (15) that model the interaction of the slider 32and the rail 13, grid search was done to find the values that resultedin the best fit of the simulation results. Equations (14) and (15) aresolved numerically in a Simulink™ model and the experimental results arepresented below. These parameters were used for estimating the behaviorof the whole mechanism.

Up to this point the model for the actuation system and the interactionbetween the slider and the rail were presented. To model the behavior ofthe platform and predict its output force and displacement we integratedthe models for the actuation system and the slider in an overalldynamical model for the platform. We verified the proposed model for thepop-up platform through experimental comparison, as reported in the nextsection. Due to the symmetry of the structure, the kinematics of thepop-up platform is similar to that of a double slider mechanism that hasbeen expanded to a triple slider and the force that the platform cangenerate on the middle part is the sum of the vertical force that threeof such triple slider mechanisms can generate. The kinematics of themechanism is dictated by the angle θ₂. These equations can be rearrangedto present all the variables as the input motion of the link 1 but thefollowing representation is more convenient in the dynamic analysis ofthe mechanism.

x ₁ =l(1−cos θ₂),{dot over (x)} ₁ =l{dot over (θ)} ₂ sin θ₂ ,{umlautover (x)} ₁=

l({umlaut over (θ)}₂ sin θ₂+{dot over (θ)}₂ ² cos θ₂)  (18)

z ₃ =l sin θ,ż ₃ =l{dot over (θ)} ₂ cos θ₂ ,{umlaut over (z)} ₃=

l({umlaut over (θ)}₂ cos θ₂−{dot over (θ)}₂ ² sin θ₂)  (19)

x ₂ =x ₁/2,{dot over (x)} ₂ ={dot over (x)} ₁/2,{umlaut over (x)} ₂={umlaut over (x)} ₁/2  (20)

z ₂ =x ₃/2,ż ₂ =ż ₃/2,{umlaut over (z)} ₂ ={umlaut over (z)} ₃/2  (21)

The free body diagrams of the three (3) links are presented in FIG. 12.The followings are the governing dynamic equations for the mechanism.

$\begin{matrix}{\mspace{79mu} {F_{y{({3 - 2})}} = {{m_{3}( {g + \overset{¨}{y_{3}}} )} + F_{{Load}\mspace{11mu} {cell}}}}} & (22) \\{\mspace{79mu} {F_{y{({1 - 2})}} = {F_{y{({3 - 2})}} + {m_{2}( {g + \overset{¨}{y_{2}}} )}}}} & (23) \\{F_{x{({1 - 2})}} = {{F_{y{({1 - 2})}}\cot \mspace{11mu} \theta_{2}} + {{1/2}\mspace{11mu} m_{2}\; \cot \mspace{11mu} \theta_{2}\overset{¨}{y_{2}}} + {{1/2}\mspace{11mu} m_{2}\overset{¨}{x_{2}}} + \frac{I_{2}\overset{¨}{\theta_{2}}}{I_{2}\sin \mspace{11mu} \theta_{2}} + {2\; k_{hinge}\mspace{11mu} \theta_{2}}}} & (24) \\{\mspace{79mu} {F_{y{({rail})}} = {F_{y{({1 - 2})}} + {m_{2}\; g} - F_{mz}}}} & (25) \\{\mspace{79mu} {{m_{1}\overset{¨}{x_{1}}} = {F_{mx} - F_{fr} - F_{x{({1 - 2})}}}}} & (26) \\{\mspace{79mu} {F_{fr} = {{{sign}\mspace{11mu} ( \overset{.}{x} )( F_{y{({rail})}} )µ_{n}} - C}}} & (27)\end{matrix}$

In the manufactured exemplary device 100 the hinges were characterizedby a b of 10 mm, L of 1 mm and h of 25 μm; the elastic module E of theKapton™ layer used was 2 GPa. Hinges were experimentally evaluated tohave a rotational stiffness k_(hinge) through repeated tests using smallweights in different angular positions. It resulted 0.84±3 10−6 Nm/rad.Equations (18-27) dictate the behavior of the mechanism. The estimationbased on them was used to study the experimental results and todetermine trends in the results for various loading and actuationscenarios.

In the following paragraphs, experiments are discussed to verify thenegligible effects such as transient thermal and electromagnetic effectsand to characterize the unknown parameters in the model (μ_(n), C, andQ). As the first set of experiments, the magnetic field flux density Bwas measured, the variation produced by the coils upon activation, asshown in FIG. 14A. W used this test to verify coil system time constantand the increase of resistance due to the temperature increase. As thesecond set of experiments, we measured the motion of a single magnetpropelled by the coils, as shown in FIG. 13C. This test set was used toevaluate the parameters affecting the rail and slider interaction suchas the friction coefficient μn, the external force C and the coilquality factor Q.

To verify the value of the time constant τ, a Hall Effect sensor, forexample the SS490, Honeywell, on the coil system and we recorded thevariation of magnetic field flux density B in time, during energizationwith input voltages of 20 V and 30 V, schematically represented in FIGS.13A and B. The sensor was placed over the coil approximatively at thecenter of the external one at a vertical distance of 1-2 mm. Becausethis test has been used to verify the time response of the system, theplacement of the coil does not have critical importance as long as theproduced field is in the sensitivity range of the sensor.

FIG. 14 shows that the experimentally evaluated time constant τ resultedaround 7 μs, smaller than the theoretical one of 11.2 μs, this is due tothe loss of some turns in the stacking process caused by the flow of theexcess of the conductive glue which reduced the ratio of the inductanceto resistance. As further shown in FIG. 14, the B field was alsomeasured over time, to verify the increment in the electrical resistancedue to the increase in temperature, by maintaining the powering voltagefor 0.2 s in order to appreciate the thermal effect thus identifying,for different voltages, its influence on the produced magnetic fieldflux density. In order to compare the model result with the experiments,because B is proportional to the current flowing in the coil I, thetheoretical normalized current decrease in time was calculated.

These factors contribute in slightly decreasing the heating rate of thecoil as FIG. 15A shows, but the linear trend in the investigated timespan confirmed the magnetic field decreases due to the increase oftemperature. The experimental results are shown in FIG. 15B, this effectcan be considered negligible in the timespan of the actuation of lessthan 0.1 s as discussed below. The experimental results show that thetransient electromagnetic behavior was too fast and the transientthermal behavior was too slow compared to the actuation time span. Soboth effects are negligible and were not be included in the model ofdevice 100.

Next, actuator tests and determination of dynamic parameters arepresented, according to still another aspect of the present invention.Friction coefficient μ_(n), the external force C, and the coil qualityfactor Q, are three parameters in the model that are highly dependent onthe fabrication precision and quality; therefore it is preferable thattheir values are verified experimentally. Here the characterization ofthese parameters are presented, by studying the motion of a singleslider as an actuator 200 as it is propelled by the coils 23 and movesalong linear motion axis LA1.

The slider motion of actuator 200 is constrained by the rail structures13, 15, 17 of openings 12, 14, 16. The input voltages from 5 V to 30 Vwith 5 V increments was applied to the coil system while recording themotion of the slider 32 with a high speed camera (FS700RH, Sony™) at 960fps. The test was repeated for three (3) times for each of the threeactuators 200 of device 100. FIG. 16B show the raw data for singlerepetition at different voltages. At 5 V the magnet was repulsed by thefirst coil and attracted by the second, in agreement with the Fx shownin FIG. 16A.

Because at this voltage the momentum that is built up was rather small,the magnet stopped before reaching the position with zero horizontalforce. At 10 V, magnet 32 built up enough momentum to surpass the zeroforce position but when it comes to a halt, the magnetic force was notlarge enough to pull it back to the zero force position. At highervoltages the magnet not only surpassed the zero force point but alsowent further, in the zone where the attraction force moved it back.Finally, at 30 V it changed direction twice before stopping. The samemotion was simulated by using the model and the parameters wereiteratively adjusted to replicate the behavior. These parameters arereported in Table V. For an easier comparison between the simulation andexperiment results, some features of the curve, stroke versus time, wereevaluated in both simulations and experiments and were used for thecomparison. In FIG. 16C, the characteristics maximum position, finalposition, maximum speed and motion time are highlighted. Experimentalresults that combine the different rails outcome were compared with themodel results where the average of the μ_(rs), μ_(rs) and C parametersis used. The results of the comparison are reported in FIG. 17.

Next, the pop-up mechanism performance of device 100 and modelverification were performed. This has been done to demonstrate theeffectiveness of the actuation method, the design and the manufacturingof device 100. By comparing the model prediction of the behavior of themechanism with the test results we also confirmed the system model. Inthe first set of experiments, the motion was measured. As shown in FIG.18A, an exemplary device 100 was used with tracking markers on top ofeach magnet 32, 42, 52 of actuators 200. This device 100 was used toverify the dynamic model of the mechanism. In the second set, we loadedthe platform 80 with varying masses, as shown in FIG. 18B. This test setwas used to validate the dynamic model of the mechanism and theworkspace reduction upon changes of the payload.

Regarding the motion of the device 100, the position tracking was usedof the pop-up platform motion to demonstrate the performance of thesystem and to verify the presented model. The platform moves out of theplane upon coils activation. Input voltages from 20 V to 50 V, with 5 Vincrements, were applied to the coil system and we measured with thehigh-speed camera the top element position in time. The recording wasdone from the side of device 100, and the results of the tracking areshown in FIG. 19; platform elevation, speed and acceleration in time fordifferent input voltages are reported.

Another test was performed to verify the dynamic model of the mechanismand the workspace reduction upon changes of the payload, as shown inFIG. 18B. The same tracking as described above was performed by placingon the top platform different set of weights.

For each weight, we identified the minimum voltage to generate motionand the starting platform position, the resulting position was measuredin time with the high-speed camera. The results of the tests arereported in FIG. 20. We employed the dynamics parameters previouslydetermined, jointly with platform segments weights that are reported inTable III, and flexible hinge rotational stiffness in the modelling ofthe pop-up platform. In the model, assuming all three legs having thesame behavior, it was considered that a single leg elevates one third ofthe platform mass, in agreement with the considerations made above. InFIG. 21, the comparison of device motion experimental and theoreticalresults are presented.

From the experiment, it was shown that the speed of device 100 could beadjusted by changing the voltage. The simulated results slightlyoverestimated real performance of device 100. This is likely due to thethree legs composing the system having some variability in dynamicparameters, such as friction coefficients, and in the coils. These smalldifferences made motion initiation slightly asynchronous thus reducingplatform performance. One of the advantages of having a parallelplatform with redundant actuation is the capability of maintaining thetop platform or centerpiece 80 parallel to the base. The tests showed anaverage misalignment angle of 0.4±0.38 degrees, thus demonstrating theaccuracy of the fabrication method and the device mechanism.

Moreover, device 100 also presents a certain load carrying capacity ofthe centerpiece or platform 80. A series of tests were performed toevaluate the capability of device 100 in applying steady forces. A forcesensor (ATI™ Nano 17) was placed at increasing distances form platform80, as shown in FIG. 22. After activation, the steady forces weremeasured. The tests were repeated at different voltages (10 V to 40 V)and the results were compared with simulations, as reported in FIG. 23.We obtained maximum steady forces of 0.17 N, it appears that the modelprediction resulted more accurate for higher voltages being lesssensitive to friction forces.

Another aspect that was considered was the workspace reduction due tothe increase in payload. As an extension of the results reported in FIG.23, the model to change platform payload was used, and once fixed theminimum starting condition and voltage to generate motion, the finalposition was calculated and maximum achievable speed. As represented inFIGS. 24A and 24B, an increase in the payload limits platform achievablespeeds and its range of motion.

To briefly summarize some of the features, a portable 1.7 mm thickpop-up planar actuator device 100 is shown, that can be switched from a2D planar state to a 3D actuation state when popped up. Formanufacturing the device 100, preferably an SCM fabrication techniquecan be used, by embedding multiple essential components such as foldinglinkages and actuation system in the different layers of the structure.The device 100 has also been fully modelled and characterized by thenominally 2-D magnetic actuation system, based on planar coils. For anexemplary non-limiting embodiment, a maximum elevation of 13 mm wasachieved, with a maximum linear velocity of over 600 mm/s for theactuators 200. The actuation time for performing the configurationchange resulted lower than 0.1 s. Device 100 lays a new ground in termsof performance, size and embedment of the actuation, comparing to allbackground art solutions. Device 100 has superior performance and novelfeatures, and can be used in new application fields, such as inherentforce control of the actuators and back-drivability of the transmission,thus making it ideal for HRI haptic applications or fragile objectsmanipulation.

FIG. 25 shows a schematic perspective view of another embodiment of thepop-up foldable actuator device, where a delta robot is interfaced theactuator legs 30, 40, 50, showing the device 100 in a folded portableconfiguration on the left, and 3D pop-up configuration on the right. Inthis figure, a possible application is shown of device 100 to beinterfaced with the delta robot principle. The delta robot structurethat is movably connected to the device 100 includes a first, a second,and a third articulated arm and a centerpiece pivotably connected toeach of the first, second, and third articulated arm, each of the first,second, and third articulated arm having a lower section and an uppersection pivotably connected to each other, each end portion of thefirst, the second, and the third middle section of the first, thesecond, and the third leg, respectively, pivotably connected to thelower section of the first, second, and third articulated arm,respectively.

FIG. 26A-26C shows a schematic perspective views of the pop-up foldableactuator device on a slidable tray integrated into a laptop computer(FIG. 26A), into a tablet (FIG. 26B), and into a smart phone (FIG. 26C),according to still another aspect of the present invention. As thedevice 100 can be made very thin in a collapsed state, portable robotand haptic applications can be made, where the device can be collapsedto the 2D state to a tray or slide that can be slid, folded, or flippedto enter or be otherwise accommodated by a casing of, for example, butnot limited to a smart phone, tablet computer, notebook computer.

While the invention has been disclosed with reference to certainpreferred embodiments, numerous modifications, alterations, and changesto the described embodiments, and equivalents thereof, are possiblewithout departing from the sphere and scope of the invention.Accordingly, it is intended that the invention not be limited to thedescribed embodiments, and be given the broadest reasonableinterpretation in accordance with the language of the appended claims.

1. A planar actuator device, comprising: a base plate including a first,second, and third pair of planar coils, each pair of planar coils havingan inner coil and an outer coil, each pair of planar coils arrangedalong a first, second, and third linear motion axis, respectively, thefirst, second, and third linear motion axis arranged in a starconfiguration; and an actuation mechanism including a first, second, andthird planar legs and a centerpiece, the first, second and third planarlegs pivotably connected to the centerpiece, the planar legs including afirst, second, and third sliding element and a first, second, and thirdmiddle section, respectively, a sliding element and middle section of arespective leg pivotably connected to each other, each sliding elementincluding a permanent magnet, wherein the first, second and third coilpairs respectively, are configured for magnetic coupling with arespective permanent magnet of the first, second, and third slidingelement, respectively, to move the first, second, and third slidingelement along the first, second, and third linear motion axis,respectively.
 2. The planar actuator device according to claim 1,further comprising: a power supply configured to provide power to eachof the first, second, and third pair of planar coils for the magneticcoupling.
 3. The planar actuator device according to claim 1, wherein aposition of the outer coil of the first, second, and third coil pairalong the first, second and third linear motion axis, respectively, isdefined such that the first, second, and third sliding elements can bemoved outwardly away from a center of the base plate along the first,second and third linear motion axis, respectively, such that theactuation mechanism is flat, arranged in parallel with a plane definedby the base plate.
 4. The planar actuator device according to claim 1,wherein the legs and centerpiece of the actuation mechanism are madefrom a single sheet, and the permanent magnets are bonded to the singlesheet.
 5. The planar actuator device according to claim 2, furthercomprising: a controller device configured to control the power supplyfor individual power control for each coil of the first, second, andthird coil pair, to establish the magnetic coupling individually foreach coil and individual linear movement of the first, second, and thirdslider along the first, second, and third linear motion axis.
 6. Theplanar actuator device according to claim 1, further comprising: afirst, second, and third rail structure for guiding a linear motion ofthe first, second, and third sliding element along the first, second,and third linear motion axis, respectively.
 7. An actuator device,including: a base plate including a first, second, and third pair ofplanar coils, each pair of planar coils having an inner coil and anouter coil, each pair of planar coils arranged along a first, second,and third linear motion axis, respectively, the first, second, and thirdlinear motion axis arranged in a star configuration; an actuationmechanism including a first, second, and third planar legs, the planarlegs including a first, second, and third sliding element and a first,second, and third middle section, respectively, a sliding element andmiddle section of a respective leg pivotably connected to each other,each sliding element including a permanent magnet; and a delta robotstructure including a first, a second, and a third articulated arm and acenterpiece pivotably connected to each of the first, second, and thirdarticulated arm, each of the first, second, and third articulated armhaving a lower section and an upper section pivotably connected to eachother, each end portion of the first, the second, and the third middlesection of the first, the second, and the third leg, respectively,pivotably connected to the lower section of the first, second, and thirdarticulated arm, respectively.
 8. The actuator device according to claim6, wherein the upper section and the lower section of the first, second,and third articulated arm have a same length.
 9. The actuator deviceaccording to claim 6, wherein a position of the outer coil of the first,second, and third coil pair along the first, second and third linearmotion axis, respectively, is defined such that the first, second, andthird sliding elements can be moved outwardly away from a center of thebase plate along the first, second and third linear motion axis,respectively, such that the actuation mechanism and the delta robotstructure is flat, arranged in parallel with a plane defined by the baseplate.
 10. The actuator device according to claim 6, further comprising:a first, second, and third rail structure for guiding a linear motion ofthe first, second, and third sliding element along the first, second,and third linear motion axis, respectively.